Bridge mode correction system based on vehicle vibration signal

Abstract

The application discloses a bridge mode correction system based on vehicle vibration signals, which comprises a field measurement system, a data analysis processing platform and a data output and display terminal. The field measurement system comprises a measurement vehicle system, a data acquisition module, a data conversion module, a data communication module and a data storage module. The measurement vehicle system comprises a measurement vehicle and a towing vehicle. The measurement vehicle can rotate around a rotating shaft relative to the towing vehicle and can move along a sliding shaft relative to the towing vehicle. A sensor is installed on the central position of the axle of the measurement vehicle or a carriage above the central position of the axle. The data acquisition module acquires vertical acceleration response measured by the sensor, the data conversion module converts data, and the data communication module transmits data to the data storage module for storage. The data analysis processing platform is used for bridge mode identification according to the acquired vertical acceleration response data. The data output and display terminal is used for real-time output and display of the calculation results of the data analysis processing platform.

Description

Technical Field

[0001] This invention belongs to the field of bridge health monitoring technology, specifically a bridge vibration mode correction system based on vehicle vibration signals. Background Technology

[0002] Against the backdrop of vigorous development of a transportation powerhouse, an increasing number of bridges are emerging. With the widespread service of these bridge structures, structural safety and operational maintenance issues are also constantly arising. If not detected and addressed promptly, these issues can pose significant threats to the safe operation of bridges. Therefore, it is necessary to conduct health monitoring of engineering structures to detect the extent of damage, providing a basis for structural reinforcement and repair, thereby ensuring the normal operation of the structures and protecting people's lives and property. However, given the large number and wide distribution of bridge structures, how to achieve rapid, economical, and accurate condition assessment and damage diagnosis is a critical issue that urgently needs to be addressed in my country's infrastructure management.

[0003] Modal parameters (including natural frequencies, damping ratios, and mode shapes) are inherent properties of a structure, commonly used to describe its fundamental dynamic characteristics, and are widely applied in areas such as structural damage identification, finite element model updates, and structural health monitoring. Compared to natural frequencies, changes in mode shapes are more sensitive to structural damage and can be used to identify localized / minor damage, especially higher-order mode shapes. Traditional methods for obtaining structural mode shapes primarily involve deploying a series of sensors at different locations along the bridge deck and using relevant signal analysis techniques to reconstruct the bridge's mode shapes from multiple sets of responses recorded by the sensors. Due to the limitation on the number of sensors, the resulting bridge mode shapes have low spatial resolution, meaning the mode shape curves are discontinuous, which is often detrimental to damage detection in bridge structures.

[0004] In recent years, bridge condition assessment technology based on vehicle response has developed rapidly. This technology mainly involves mounting sensors on a moving test vehicle to record the vehicle's vibration signals when it crosses a bridge. Through data analysis, the modal parameters (natural frequencies, damping ratio, and mode shapes) of the bridge can be identified. This method has been favored by scholars worldwide due to its speed, economy, ease of operation, and high mobility, and its effectiveness and efficiency have been fully verified. However, this method is only suitable for bridges with relatively small structural damping ratios and cannot accurately identify bridges with large damping ratios. The main reason is that, due to the presence of the damping ratio, the envelope of the amplitude of each order of the bridge's modal response separated from the vehicle response will shrink and shift, causing the reconstructed mode shape curves to deviate completely from the theoretical mode shapes. Furthermore, the signal filtering techniques used in traditional methods suffer from phase delay, making it impossible to accurately obtain the modal responses of each order of the bridge. This leads to boundary effects in the extracted modal response amplitudes, interfering with engineers' ability to locate bridge damage. Summary of the Invention

[0005] Therefore, the bridge mode correction system based on vehicle vibration signals is provided, which can eliminate the contraction and deviation effects caused by the structural damping ratio and realize accurate identification of the damping bridge mode.

[0006] To achieve the above-mentioned purpose, the technical scheme is provided as follows.

[0007] The bridge mode correction system based on vehicle vibration signals comprises a field measurement system, a data analysis processing platform and a data output and display terminal.

[0008] The field measurement system comprises a measurement vehicle system, a data acquisition module, a data conversion module, a data communication module and a data storage module; the measurement vehicle system comprises a measurement vehicle and a towing vehicle; the towing vehicle is used to guide the movement of the measurement vehicle; the measurement vehicle can rotate relative to the towing vehicle around a rotating shaft and can move relative to the towing vehicle along a sliding shaft; the rotating shaft and the sliding shaft are perpendicular to each other; the measurement vehicle comprises a vehicle compartment; a vehicle axle is installed on the vehicle compartment; the vehicle axle is perpendicular to the rotating shaft and the sliding shaft; a sensor is installed on the central position of the vehicle axle or the vehicle compartment directly above the central position of the vehicle axle; the data acquisition module acquires the vertical acceleration response measured by the sensor; the data conversion module converts the acquired vertical acceleration response data; and the data communication module transmits the converted vertical acceleration response data to the data storage module for storage.

[0009] The data analysis processing platform is used to identify the bridge mode according to the acquired vertical acceleration response data.

[0010] The data output and display terminal is used to output and display the calculation results of the data analysis processing platform in real time.

[0011] Further, the rotating shaft is rotationally connected with the towing vehicle; a sliding sleeve is arranged on the rotating shaft; the sliding shaft is slidingly connected with the sliding sleeve; and the sliding shaft is fixedly installed on the vehicle compartment.

[0012] Further, the method for the field measurement system to acquire the vertical acceleration response data is as follows:

[0013] 11) The sensor is arranged at the central position of the vehicle axle of the measurement vehicle or on the vehicle compartment directly above the central position of the vehicle axle of the measurement vehicle;

[0014] 12) The towing vehicle is used to guide the measurement vehicle to uniformly move over the bridge to be measured; and the vertical acceleration response detected by the sensor is recorded during the movement of the measurement vehicle over the bridge to be measured. .

[0015] Further, the bridge mode identification method based on the collected vertical acceleration response data is:

[0016] 21) Construct the balance equation of the vehicle and the bridge, and obtain the analytical expression of the measured vehicle vertical acceleration response ;

[0017] 22) Obtain the natural frequency range of the bridge to be measured by the vertical acceleration response ;

[0018] 23) Based on the natural frequency range of the bridge, the bridge modal component separated from the measured vehicle vertical acceleration response is obtained by using the zero-phase filtering method;

[0019] 24) The instantaneous amplitude of each order modal component of the bridge is extracted by using Hilbert transform ;

[0020] 25) The instantaneous amplitude is corrected by using the proposed method , and the bridge mode free from the influence of bridge damping is obtained.

[0021] Further, in step 21), the balance equation of the vehicle and the bridge is:

[0022]

[0023]

[0024] wherein, is the unit length mass of the bridge; is the damping coefficient of the bridge; is the bending stiffness of the bridge; represents the contact force between the vehicle and the bridge; is the Dirac function; is the mass of the measured vehicle; is the stiffness of the measured vehicle; and are the vertical displacements of the bridge to be measured and the measured vehicle, respectively; represents the first order derivative of ; represents the second order derivative of ; represents the fourth order derivative of x; represents the vertical acceleration response of the measured vehicle; represents the distance of the vehicle from the bridge entry point; represents time; represents the speed of the measured vehicle driving on the bridge to be measured; is the contact displacement between the bridge and the vehicle;

[0025] The vertical acceleration response of the bridge is solved as

[0026]

[0027] wherein, is the velocity parameter; is the static displacement caused by the vehicle-induced bridge vibration; is the length of the bridge; is the acceleration of gravity; is the modal order of the bridge; and are the natural frequency, the damped frequency and the damping ratio of the measured bridge, respectively; is the coefficient related to the vibration replication of the measured bridge; is the phase angle; is the natural frequency of the vehicle.

[0028] Further, in the step 22), the natural frequency of the measured bridge is expressed as

[0029]

[0030] wherein, is the natural frequency of the measured bridge; is the frequency; is the vertical acceleration response of the bridge; is the discrete sampling point from 0 to ; is the total length of the signal to be analyzed; is the imaginary unit.

[0031] Further, in the step 23), the zero-phase filtering method process is as follows:

[0032] The sequence is input to the filter to generate the filtered signal :

[0033]

[0034] The filtered signal is reversed to obtain the signal :

[0035]

[0036] The signal is inverse filtered to obtain the signal​​ :

[0037]

[0038] flip the signal to get the output signal : :

[0039]

[0040] obtain the zero-phase output signal, i.e. the modal components of the bridge :

[0041]

[0042] wherein, is defined as the corresponding transform in the time domain.

[0043] Further, in the step 24), the instantaneous amplitude is expressed as:

[0044]

[0045] wherein, denotes the transform pair of the modal components of the bridge :

[0046] Further, in the step 25), the correction method of the instantaneous amplitude comprises the following steps:

[0047] 251) perform a reflection transform on the instantaneous amplitude on the axis to obtain a reflected amplitude :

[0048]

[0049] 252) perform a translation transform on the obtained reflected amplitude : i.e. translate the reflected amplitude L / v units of length to the right along the axis to obtain a translated amplitude :

[0050]

[0051] 253) since and have the same range of values, replace with to obtain the instantaneous amplitude​ multiplied by the translation amplitude to obtain the modified bridge mode shape :

[0052]

[0053] wherein, represents the amplitude of the modified mode shape.

[0054] The present application has the following advantages:

[0055] The bridge mode shape modification system based on vehicle vibration signals of the present application is characterized in that the measurement vehicle is arranged to rotate around a rotation shaft relative to the towing vehicle and to move along a sliding shaft relative to the towing vehicle, and the rotation shaft and the sliding shaft are both perpendicular to the axle of the measurement vehicle. In this way, during the process of guiding the measurement vehicle to walk on the bridge to be measured by the towing vehicle, the displacement, speed and acceleration of the measurement vehicle during the driving process can be measured by the sensors arranged at the central position of the axle or on the carriage above the central position of the axle, and then the vertical acceleration response data of the measurement vehicle during the driving process on the bridge to be measured can be obtained. Then, the bridge mode shape is identified according to the collected vertical acceleration response data by the data analysis and processing platform, and is displayed in real time by the data output and display terminal. In summary, the bridge mode shape modification system based on vehicle vibration signals of the present application can eliminate the contraction and offset effects caused by the structural damping ratio, and realize the accurate identification of the modal shape of the damping bridge.

[0056] Specifically, in the method of identifying the bridge mode shape according to the collected vertical acceleration response data by the data analysis and processing platform, the vertical acceleration response is measured by the sensors, and then the analytical expression of the vertical acceleration response is obtained by the balance equation of the vehicle and the bridge. Then, the bridge modal component is separated from the vertical acceleration response of the measurement vehicle by the zero-phase filtering method, so as to eliminate the phase distortion of the separated bridge modal response and obtain the "high-fidelity" bridge component response. After the instantaneous amplitude of each modal component of the bridge is extracted by the Hilbert transform, the instantaneous amplitude is modified to eliminate the contraction and offset effects caused by the structural damping ratio, and the accurate identification of the modal shape of the damping bridge is realized, so as to further use the modal shape of the bridge for the damage identification of the bridge. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application provides the following drawings for illustration:

[0058] Figure 1A schematic diagram of the principle of the bridge mode correction system based on vehicle vibration signals according to the present application;

[0059] Figure 2 A structural schematic diagram of the measurement vehicle system;

[0060] Figure 3 A mathematical model of the bridge to be measured;

[0061] Figure 4 Bridge modes identified under different structural damping ratios;

[0062] Figure 5 Bridge modes identified under different vehicle speeds;

[0063] Figure 6 Bridge modes identified under high-order (second and third order) modes of the bridge;

[0064] Figure 7 Bridge modes identified under a three-span continuous bridge. DETAILED DESCRIPTION

[0065] The present application will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it.

[0066] As shown in Figure 1 the present embodiment, the bridge mode correction system based on vehicle vibration signals comprises a field measurement system, a data analysis processing platform, and a data output and display terminal.

[0067] In the present embodiment, the field measurement system comprises a measurement vehicle system, a data acquisition module, a data conversion module, a data communication module, and a data storage module. The measurement vehicle system of the present embodiment is used to measure vertical acceleration response data in real time, the data acquisition module acquires vertical acceleration response data measured by sensors, the data conversion module converts the acquired vertical acceleration response data, and the data communication module transmits the converted vertical acceleration response data to the data storage module for storage. As shown in Figure 2As shown, the measurement vehicle system of the embodiment comprises a measurement vehicle 10 and a towing vehicle 11 for guiding the movement of the measurement vehicle 10, and the measurement vehicle 10 can rotate relative to the towing vehicle 11 around a rotation shaft 12 and can move relative to the towing vehicle 11 along a sliding shaft 13, the rotation shaft 12 and the sliding shaft 13 being perpendicular to each other. In the embodiment, the rotation shaft 12 is rotationally coupled with the towing vehicle 11, the rotation shaft 12 is provided with a sliding sleeve, the sliding shaft 13 is slidingly coupled with the sliding sleeve, and the sliding shaft 13 is fixedly connected with the measurement vehicle 10. The measurement vehicle 10 comprises a vehicle compartment 16, a vehicle axle 14 is installed on the vehicle compartment 16, the vehicle axle 14 is perpendicular to the rotation shaft 12 and the sliding shaft 13, and the sliding shaft 13 is fixedly installed on the vehicle compartment 16. In the embodiment, a sensor 15 for collecting acceleration data of the measurement vehicle 10 during the driving of the measurement vehicle 10 on the bridge to be measured is arranged at the central position of the vehicle axle 14. Of course, in other embodiments, the sensor 15 can also be arranged on the vehicle compartment 16 directly above the central position of the vehicle axle 14.

[0068] Specifically, in the embodiment, the method for collecting vertical acceleration response data by the field measurement system is as follows:

[0069] 11) The sensor 15 is arranged at the central position of the vehicle axle 14 of the measurement vehicle 10 or on the vehicle compartment 16 directly above the central position of the vehicle axle 15 of the measurement vehicle 10;

[0070] 12) The towing vehicle 11 is used to guide the measurement vehicle 10 to drive at a constant speed on the bridge to be measured, and the vertical acceleration response data detected by the sensor 15 during the driving of the measurement vehicle 10 on the bridge to be measured is recorded. .

[0071] In the embodiment, the data analysis processing platform is used to identify the bridge mode according to the collected vertical acceleration response data. Specifically, the method for identifying the bridge mode by the data analysis processing platform according to the collected vertical acceleration response data is as follows:

[0072] 21) A balance equation of the vehicle and the bridge is constructed, and an analytical expression of the vertical acceleration response of the measurement vehicle is solved.

[0073] Specifically, the balance equation of the vehicle and the bridge is as follows:

[0074]

[0075]

[0076] wherein, is the unit length mass of the bridge; is the damping coefficient of the bridge; is the bending stiffness of the bridge; represents the contact force between the vehicle and the bridge; is the Dirac function;​ to measure the mass of the vehicle; to measure the stiffness of the vehicle; and respectively represent the vertical displacement of the bridge and the measuring vehicle; represents the first derivative of ; represents the second derivative of ; represents the fourth derivative of x; represents the vertical acceleration response of the measuring vehicle; represents the distance of the vehicle from the bridge entry point; represents time; represents the speed of the measuring vehicle on the bridge under test; is the contact displacement between the bridge and the vehicle;

[0077] the analytical expression of the vertical acceleration response obtained by solving is:

[0078]

[0079] wherein represents the speed parameter; represents the static displacement of the bridge due to the vehicle-induced vibration; represents the length of the bridge; represents the gravitational acceleration; represents the modal order of the bridge; , and respectively represent the natural frequency, the damped frequency and the damping ratio of the bridge under test; is a coefficient related to the vibration replication of the bridge under test; represents the phase angle; represents the natural frequency of the vehicle.

[0080] 22) The natural frequency range of the bridge under test is obtained by the vertical acceleration response .

[0081] In particular, the natural frequency of the bridge under test is expressed as:

[0082]

[0083] wherein represents the natural frequency of the bridge under test; represents the frequency; represents the vertical acceleration response of the bridge; is a discrete sampling point from 0 to . total length of the signal to be analyzed; denotes the imaginary unit.

[0084] 23) Based on the bridge natural frequency range, the zero-phase filtering method is used to separate the bridge modal components from the vertical acceleration response of the measuring vehicle . .

[0085] Specifically, the process of the zero-phase filtering method is as follows:

[0086] input the sequence to the filter to generate the filtered signal :

[0087]

[0088] flip the filtered signal to obtain the signal :

[0089]

[0090] inverse filter the signal to obtain the signal :

[0091]

[0092] flip the signal to obtain the output signal :

[0093]

[0094] After processing the vertical acceleration response using the zero-phase filtering method, the zero-phase output signal, i.e. the modal components of the bridge :

[0095]

[0096] wherein, is defined as the corresponding transform in the time domain.

[0097] 24) Use Hilbert transform to extract the instantaneous amplitude of each modal component of the bridge .

[0098] Specifically, the instantaneous amplitude is expressed as:

[0099]

[0100] wherein, denotes the bridge modal component of the i-th mode

[0101] It can be seen that the obtained instantaneous amplitude contains the bridge damping which will cause shrinkage and offset effects on the bridge mode shape.

[0102] 25) Correcting the instantaneous amplitude to obtain the bridge mode shape without the bridge damping.

[0103] Specifically, the correction method of the instantaneous amplitude includes the following steps:

[0104] 251) Perform a reflection transformation on the instantaneous amplitude on the axis to obtain the reflected amplitude :

[0105]

[0106] 252) Perform a translation transformation on the obtained reflected amplitude : that is, translate the reflected amplitude right along the axis by L / v units of length to obtain the translated amplitude :

[0107]

[0108] 253) Since and have the same value range, replace with , multiply the instantaneous amplitude by the translated amplitude to obtain the corrected bridge mode shape :

[0109]

[0110] wherein, denotes the amplitude of the corrected mode shape.

[0111] As can be seen from the expression of the bridge mode shape , the correction process of the bridge mode shape does not require additional bridge information, such as the difficult-to-accurately-identify damping ratio; the bridge mode shape identification only needs the vehicle body response recorded by a single sensor, and the continuous (high-resolution) bridge mode shape can be accurately reconstructed through the above transformation.

[0112] ​In this embodiment, the data output and display terminal is used to output and display the calculation results of the data analysis and processing platform in real time.

[0113] The bridge mode correction system based on vehicle vibration signals of the present invention will be described below with specific examples.

[0114] In numerical verification, the following methods are adopted: Figure 3 The mathematical model of the bridge under test is shown. Figure 3 The parameters of the bridge under test are set as follows: bridge length L = 25 m, cross-sectional dimension A = 3.2 m. 2 The bridge density is ρ = 4800 kg / m³ 3 The elastic modulus E = 2.75 × 10⁻⁶ 10 N / m 2 The parameters for the measuring vehicle are set as follows: vehicle stiffness k v = 200 kN / m, vehicle mass m v = 14,000 kg, moving speed v = 2 m / s. Given the bridge parameters, the theoretical values ​​for the first two frequencies of the bridge can be calculated as 1.39 Hz and 5.56 Hz, respectively.

[0115] To verify the versatility of the bridge mode correction system based on vehicle vibration signals in this embodiment, numerical verification showed its effectiveness across bridges with different damping ratios, varying speeds, different modal orders, and different structural forms. Specifically, this embodiment simulated bridge surface roughness identification under the following four working conditions:

[0116] Condition 1: Bridge vibration modes identified under different structural damping ratios, such as Figure 4 As shown;

[0117] Working Condition 2: Bridge vibration modes identified under different vehicle speeds, such as Figure 5 As shown;

[0118] Working condition 3: Bridge vibration modes identified under different orders of conditions, such as Figure 6 As shown;

[0119] Working Condition 4: Identification of bridge vibration modes under the condition of a three-span continuous bridge, such as Figure 7 As shown.

[0120] From the numerical verification results of the four working conditions, it can be seen that the vibration mode results obtained by the bridge vibration mode correction system based on the vehicle vibration signal in the embodiment are highly consistent with the theoretical values, and the obtained vibration modes have extremely high spatial resolution, can be used as a reliable index for bridge damage detection, and prove that the bridge vibration mode correction system based on the vehicle vibration signal in the embodiment has wide applicability, the identification process is efficient, the identification process is simple, the identification result is accurate, can provide new technical support for large-scale bridge structure vibration mode identification, serve bridge health monitoring, operation management and maintenance.

[0121] The above-described embodiments are only preferred embodiments for fully illustrating the present application, and the protection scope of the present application is not limited thereto. Any equivalent replacement or transformation made by those skilled in the art on the basis of the present application is within the protection scope of the present application. The protection scope of the present application is subject to the claims.

Claims

1. A bridge mode correction system based on vehicle vibration signals, characterized in that: This includes on-site measurement systems, data analysis and processing platforms, and data output and display terminals; The field measurement system includes a measurement vehicle system, a data acquisition module, a data conversion module, a data communication module, and a data storage module. The measurement vehicle system includes a measurement vehicle and a tractor. The tractor guides the measurement vehicle's movement, and the measurement vehicle can rotate relative to the tractor around a pivot axis and move relative to the tractor along a sliding axis, the pivot axis and the sliding axis being perpendicular to each other. The measurement vehicle includes a carriage with an axle mounted on it, the axle being perpendicular to both the pivot axis and the sliding axis. A sensor is mounted at the center of the axle or on the carriage directly above the center of the axle. The data acquisition module acquires the vertical acceleration response measured by the sensor. The data conversion module converts the acquired vertical acceleration response data. The data communication module transmits the converted vertical acceleration response data to the data storage module for storage. The data analysis and processing platform is used to identify bridge vibration modes based on the collected vertical acceleration response data; The data output and display terminal is used to output and display the calculation results of the data analysis and processing platform in real time; The method used by the data analysis and processing platform to identify bridge vibration modes based on the collected vertical acceleration response data is as follows: 21) Construct the equilibrium equations for the vehicle and the bridge, and solve for the vertical acceleration response of the measuring vehicle. The analytical expression; 22) Through vertical acceleration response The natural frequency range of the bridge under test is obtained; 23) Based on the bridge's natural frequency range, the vertical acceleration response of the measuring vehicle is obtained using a zero-phase filtering method. The bridge modal components obtained from the separation ; 24) Extract the instantaneous amplitude of each modal component of the bridge using Hilbert transform. : 25) Correct the instantaneous amplitude using the proposed method. The bridge vibration mode affected by immune bridge damping was obtained.

2. The bridge mode correction system based on vehicle vibration signals according to claim 1, characterized in that: The rotating shaft is rotatably engaged with the tractor vehicle. The rotating shaft is provided with a sliding sleeve, and the sliding shaft is slidably engaged with the sliding sleeve. The sliding shaft is fixedly installed on the carriage.

3. The bridge mode correction system based on vehicle vibration signals according to claim 1 or 2, characterized in that: The method for acquiring vertical acceleration response data by the field measurement system is as follows: 11) Place the sensor at the center of the measuring vehicle's axle or on the carriage directly above the center of the measuring vehicle's axle; 12) Use a tractor to guide the measuring vehicle to travel at a constant speed across the bridge to be measured. While the measuring vehicle is traveling on the bridge, record the vertical acceleration response detected by the sensors. .

4. The bridge mode correction system based on vehicle vibration signals according to claim 1, characterized in that: In step 21), the equilibrium equations for the vehicle and the bridge are: in, The mass per unit length of the bridge; This is the damping coefficient of the bridge; For the bending stiffness of the bridge; This indicates the contact force between the vehicle and the axle; It is the Dirac function; To measure the mass of the vehicle; To measure the rigidity of the vehicle; and These represent the vertical displacements of the bridge under test and the measuring vehicle, respectively. express right The first derivative; express right The second derivative; Indicate The fourth derivative with respect to x; This indicates the vertical acceleration response of the measuring vehicle; Indicates the distance of the vehicle from the bridge entry point; Indicates time; This indicates the speed at which the measuring vehicle travels on the bridge being measured. This refers to the contact displacement between the bridge and the vehicle. The vertical acceleration response obtained by solving The analytical expression is: in, , represents the speed parameter; , representing the static displacement caused by vehicle-induced bridge vibration; Indicates the length of the bridge; Represents gravitational acceleration; Indicates the modal order of the bridge; , and These are the natural frequency, damping frequency, and damping ratio of the bridge under test, respectively. The coefficients related to the replication of the vibration of the bridge under test; Indicates the phase angle; This indicates the vehicle's natural frequency.

5. The bridge mode correction system based on vehicle vibration signals according to claim 4, characterized in that: In step 22), the natural frequency of the bridge under test is expressed as: in, Indicates the natural frequency of the bridge under test; Indicates frequency; This indicates the vertical acceleration response of the bridge; From 0 Discrete sampling points; The total length of the signal to be analyzed; It represents the imaginary unit.

6. The bridge mode correction system based on vehicle vibration signals according to claim 5, characterized in that: In step 23), the zero-phase filtering method process is as follows: will sequence Input to filter To generate filtered signals : For the filtered signal Flip the signal to obtain the signal. : For signal The signal is obtained by performing inverse filtering. : For signal The signal is flipped to obtain the output signal. : Vertical acceleration response After processing using the zero-phase filtering method, a zero-phase output signal is obtained, which represents the modal components of the bridge. : in, Defined as the corresponding time domain Transformation.

7. The bridge mode correction system based on vehicle vibration signals according to claim 6, characterized in that: In step 24), instantaneous amplitude Represented as: in, Represents the modal components of the bridge. Transformation pairs.

8. The bridge mode correction system based on vehicle vibration signals according to claim 7, characterized in that: In step 25), instantaneous amplitude The correction method includes the following steps: 251) For instantaneous amplitude exist Perform a reflection transformation on the axis to obtain the reflection amplitude. : 252) Regarding the obtained reflection amplitude Perform a translation transformation: that is, the reflection amplitude Along The translation magnitude is obtained by shifting the axis to the right by L / v units. : 253) Due to and Having the same range of values, using replace Instantaneous amplitude With translation amplitude Multiplying them together yields the corrected bridge vibration mode. : in, This represents the amplitude of the modified mode shape.

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